Accurate relativistic chiral nucleon-nucleon interaction up to NNLO

Abstract: We construct a relativistic chiral nucleon-nucleon interaction up to the next-to-next-to-leading order in covariant baryon chiral perturbation theory. We show that a good description of the $np$ phase shifts up to $T_\mathrm{lab}=200$ MeV and even higher can be achieved with a $\tilde{\chi}^2/\mathrm{d.o.f.}$ less than 1. Both the next-to-leading order results and the next-to-next-to-leading order results describe the phase shifts equally well up to $T_\mathrm{lab}=200$ MeV, but for higher energies, the latter behaves better, showing satisfactory convergence. The relativistic chiral potential provides the most essential inputs for relativistic ab initio studies of nuclear structure and reactions, which has been in need for almost two decades.